In this work we study the problem of secure communication over a fully quantum Gel’fand-Pinsker channel. The best known achievability rate for this channel model in the classical case was proven by Goldfeld, Cuff and Permuter, and here we generalize their result. One key feature of the results obtained in this work is that all the bounds are based on error exponents. We obtain our achievability result via the technique of simultaneous pinching. This in turn allows us to show the existence of a simultaneous decoder. Further, to obtain our encoding technique and to prove the security feature of our coding scheme we prove a bivariate classical-quantum channel resolvability lemma and a conditional classical-quantum channel resolvability lemma. As a byproduct of the achievability result obtained in this work, we also obtain an achievable rate for a fully quantum Gel’fand-Pinsker channel in the absence of Eve. The form of this achievable rate matches with its classical counterpart. The Gel’fand-Pinsker channel model had earlier only been studied for the classical-quantum case and in the case where Alice (the sender) and Bob (the receiver) have shared entanglement between them.

中文翻译：

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通过完全量子 Gel'fand-Pinsker 窃听通道的安全通信

在这项工作中，我们研究了全量子 Gel'fand-Pinsker 通道上的安全通信问题。Goldfeld、Cuff 和 Permuter 证明了经典案例中该通道模型最著名的可实现率，在这里我们概括了他们的结果。在这项工作中获得的结果的一个关键特征是所有的界限都基于误差指数。我们通过同时捏合技术获得了可实现性结果。这反过来又使我们能够展示同步解码器的存在。此外，为了获得我们的编码技术并证明我们编码方案的安全特征，我们证明了一个二元经典量子信道可解析性引理和一个条件经典量子信道可解析性引理。作为这项工作中获得的可实现性结果的副产品，我们还获得了在没有 Eve 的情况下完全量子 Gel'fand-Pinsker 通道的可实现速率。这种可实现速率的形式与其经典对应物相匹配。Gel'fand-Pinsker 通道模型之前仅针对经典量子情况以及 Alice（发送方）和 Bob（接收方）共享纠缠的情况进行了研究。